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A047381
Numbers that are congruent to {0, 1, 2, 4, 5} mod 7.
2
0, 1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78
OFFSET
1,3
FORMULA
a(n) = floor( (7/5)(n-1) ). [Gary Detlefs, Feb 20 2010]
From R. J. Mathar, Mar 11 2011: (Start)
a(n) = a(n-1) + a(n-5) - a(n-6).
G.f.: x^2*(1 + x + 2*x^2 + x^3 + 2*x^4) / ((x^4 + x^3 + x^2 + x + 1)*(x-1)^2). (End)
5*a(n) = 7*n-9-b(n) where b(n) = b(n-5) = 1, -2, 0, 2, -1 (for offset 0). - R. J. Mathar, Jul 22 2020
MAPLE
seq(floor((7/5)*(n-1)), n=1..56); # Gary Detlefs, Feb 20 2010
MATHEMATICA
CoefficientList[Series[x (1 + x + 2 x^2 + x^3 + 2 x^4) / ((x^4 + x^3 + x^2 + x + 1) (x - 1)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 26 2013 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 7}, 80] (* Harvey P. Dale, Oct 04 2023 *)
PROG
(Magma) [ n: n in [1..80] | n mod 7 in [0, 1, 2, 4, 5] ]; // Vincenzo Librandi, Jul 26 2013
CROSSREFS
Sequence in context: A346128 A276220 A288204 * A286428 A329996 A258833
KEYWORD
nonn,easy
EXTENSIONS
Formula and Maple code adapted to the offset by Wesley Ivan Hurt, Jul 16 2013
STATUS
approved